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Q. A wave has a frequency of 10 Hz and a wavelength of 2 m. What is its speed? (2023)

A. 5 m/s
B. 10 m/s
C. 20 m/s
D. 15 m/s

Solution

The speed v of a wave is given by v = fλ. Therefore, v = 10 Hz * 2 m = 20 m/s.

Correct Answer: C — 20 m/s

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Q. A wave has a frequency of 10 Hz and a wavelength of 5 m. What is its speed? (2020)

A. 50 m/s
B. 10 m/s
C. 2 m/s
D. 5 m/s

Solution

Speed (v) = frequency (f) × wavelength (λ) = 10 Hz × 5 m = 50 m/s.

Correct Answer: A — 50 m/s

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Q. A wave has a frequency of 50 Hz and a speed of 340 m/s. What is its wavelength? (2021)

A. 6.8 m
B. 7.0 m
C. 7.5 m
D. 8.0 m

Solution

Wavelength λ is given by λ = v/f. Thus, λ = 340 m/s / 50 Hz = 6.8 m.

Correct Answer: A — 6.8 m

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Q. A wave has a frequency of 50 Hz and a wavelength of 2 m. What is the speed of the wave? (2021)

A. 25 m/s
B. 50 m/s
C. 100 m/s
D. 200 m/s

Solution

The speed of a wave is given by the formula v = fλ. Here, v = 50 Hz * 2 m = 100 m/s.

Correct Answer: B — 50 m/s

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Q. A wave has a frequency of 500 Hz and a wavelength of 0.5 m. What is the speed of the wave? (2023)

A. 250 m/s
B. 500 m/s
C. 1000 m/s
D. 2000 m/s

Solution

The speed of the wave can be calculated using the formula v = fλ. Here, v = 500 Hz * 0.5 m = 250 m/s.

Correct Answer: B — 500 m/s

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Q. A wave has a frequency of 500 Hz and a wavelength of 0.6 m. What is the speed of the wave? (2022)

A. 300 m/s
B. 500 m/s
C. 600 m/s
D. 400 m/s

Solution

Using the wave equation v = fλ, we find v = 500 Hz * 0.6 m = 300 m/s.

Correct Answer: A — 300 m/s

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Q. A wave has a frequency of 500 Hz and a wavelength of 0.68 m. What is the speed of the wave? (2021)

A. 340 m/s
B. 500 m/s
C. 680 m/s
D. 250 m/s

Solution

The speed of the wave can be calculated using the formula v = fλ. Thus, v = 500 Hz * 0.68 m = 340 m/s.

Correct Answer: A — 340 m/s

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Q. A wave has a frequency of 60 Hz and a wavelength of 1.5 m. What is its speed? (2022)

A. 90 m/s
B. 60 m/s
C. 40 m/s
D. 30 m/s

Solution

Speed (v) = frequency (f) × wavelength (λ) = 60 Hz × 1.5 m = 90 m/s.

Correct Answer: A — 90 m/s

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Q. A wave has a frequency of 60 Hz and a wavelength of 3 m. What is its speed? (2016)

A. 180 m/s
B. 120 m/s
C. 60 m/s
D. 90 m/s

Solution

Speed v = f × λ = 60 Hz × 3 m = 180 m/s.

Correct Answer: A — 180 m/s

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Q. A wave has a frequency of 60 Hz and a wavelength of 3 m. What is the speed of the wave?

A. 180 m/s
B. 120 m/s
C. 60 m/s
D. 30 m/s

Solution

The speed v of a wave is given by v = fλ. Thus, v = 60 * 3 = 180 m/s.

Correct Answer: B — 120 m/s

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Q. A wave has a speed of 300 m/s and a frequency of 150 Hz. What is its wavelength? (2022)

A. 1 m
B. 2 m
C. 3 m
D. 4 m

Solution

Wavelength λ can be calculated using the formula λ = v/f. Therefore, λ = 300 m/s / 150 Hz = 2 m.

Correct Answer: B — 2 m

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Q. A wave has a wavelength of 0.5 m and a frequency of 300 Hz. What is its speed? (2020)

A. 150 m/s
B. 300 m/s
C. 600 m/s
D. 1200 m/s

Solution

Speed (v) = frequency (f) × wavelength (λ) = 300 Hz × 0.5 m = 150 m/s.

Correct Answer: A — 150 m/s

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Q. A wave on a string has a frequency of 10 Hz and a wavelength of 2 m. What is the speed of the wave? (2022)

A. 5 m/s
B. 10 m/s
C. 15 m/s
D. 20 m/s

Solution

Wave speed v is given by v = fλ. Thus, v = 10 Hz * 2 m = 20 m/s.

Correct Answer: B — 10 m/s

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Q. A wave on a string has a frequency of 60 Hz and a wavelength of 0.5 m. What is the speed of the wave? (2021)

A. 30 m/s
B. 60 m/s
C. 120 m/s
D. 15 m/s

Solution

Speed (v) = Frequency (f) × Wavelength (λ) = 60 Hz × 0.5 m = 30 m/s.

Correct Answer: C — 120 m/s

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Q. A wave on a string has a speed of 50 m/s and a wavelength of 2 m. What is its frequency? (2018)

A. 25 Hz
B. 50 Hz
C. 100 Hz
D. 75 Hz

Solution

Frequency f = v/λ = 50 m/s / 2 m = 25 Hz.

Correct Answer: A — 25 Hz

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Q. A wave on a string is described by the equation y(x, t) = 0.05 sin(2π(0.1x - 5t)). What is the amplitude of the wave?

A. 0.01 m
B. 0.05 m
C. 0.1 m
D. 0.2 m

Solution

The amplitude of the wave is the coefficient in front of the sine function. Here, the amplitude is 0.05 m.

Correct Answer: B — 0.05 m

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Q. A wave pulse travels along a string and reflects off a fixed end. What happens to the wave upon reflection? (2021)

A. It inverts
B. It remains unchanged
C. It doubles in amplitude
D. It disappears

Solution

When a wave pulse reflects off a fixed end, it inverts due to the boundary condition at the fixed end.

Correct Answer: A — It inverts

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Q. A wave traveling along a string has a frequency of 50 Hz and a wavelength of 2 m. What is the speed of the wave? (2020)

A. 25 m/s
B. 50 m/s
C. 100 m/s
D. 75 m/s

Solution

Speed (v) = frequency (f) × wavelength (λ) = 50 Hz × 2 m = 100 m/s.

Correct Answer: C — 100 m/s

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Q. A wave travels in a medium with a speed of 300 m/s and has a frequency of 75 Hz. What is the wavelength? (2021)

A. 4 m
B. 2 m
C. 3 m
D. 1 m

Solution

Wavelength λ = v/f = 300 m/s / 75 Hz = 4 m.

Correct Answer: A — 4 m

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Q. A wave travels through a medium with a speed of 500 m/s and has a wavelength of 5 m. What is its frequency? (2021)

A. 100 Hz
B. 50 Hz
C. 200 Hz
D. 250 Hz

Solution

Frequency (f) = speed (v) / wavelength (λ) = 500 m/s / 5 m = 100 Hz.

Correct Answer: A — 100 Hz

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Q. A wave travels through a medium with a speed of 500 m/s and has a wavelength of 2 m. What is its frequency? (2022)

A. 250 Hz
B. 500 Hz
C. 1000 Hz
D. 2000 Hz

Solution

Using the wave equation v = fλ, we can find frequency f = v/λ = 500 m/s / 2 m = 250 Hz.

Correct Answer: A — 250 Hz

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Q. A wave travels with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength? (2020)

A. 2 m
B. 1.5 m
C. 3 m
D. 0.5 m

Solution

Wavelength (λ) = Speed (v) / Frequency (f) = 300 m/s / 150 Hz = 2 m.

Correct Answer: A — 2 m

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Q. A wave travels with a speed of 340 m/s and has a frequency of 170 Hz. What is its wavelength? (2022)

A. 2.0 m
B. 1.0 m
C. 0.5 m
D. 3.0 m

Solution

Wavelength λ = v/f = 340 m/s / 170 Hz = 2.0 m.

Correct Answer: A — 2.0 m

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Q. A wheel is rotating with an angular acceleration of 2 rad/s². If it starts from rest, what will be its angular velocity after 5 seconds? (2022)

A. 5 rad/s
B. 10 rad/s
C. 15 rad/s
D. 20 rad/s

Solution

Using the formula ω = ω₀ + αt, where ω₀ = 0, α = 2 rad/s², and t = 5 s, we get ω = 0 + 2*5 = 10 rad/s.

Correct Answer: B — 10 rad/s

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Q. A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2 rad/s², what will be its angular velocity after 5 seconds? (2023)

A. 20 rad/s
B. 10 rad/s
C. 15 rad/s
D. 25 rad/s

Solution

Using the formula ω = ω₀ + αt, we have ω = 10 rad/s + (2 rad/s²)(5 s) = 20 rad/s.

Correct Answer: A — 20 rad/s

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Q. A wheel of radius 0.5 m is rotating with an angular speed of 10 rad/s. What is the linear speed of a point on the edge of the wheel? (2022)

A. 5 m/s
B. 10 m/s
C. 15 m/s
D. 20 m/s

Solution

Linear speed v = rω = 0.5 m * 10 rad/s = 5 m/s.

Correct Answer: B — 10 m/s

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Q. A wheel of radius R and mass M is rolling without slipping on a horizontal surface. If it has a linear speed v, what is its total kinetic energy? (2022)

A. (1/2)Mv²
B. (1/2)Mv² + (1/2)(Iω²)
C. (1/2)Mv² + (1/2)(Mv²)
D. (1/2)Mv² + (1/2)(Mv²/2)

Solution

The total kinetic energy is the sum of translational and rotational kinetic energy. K.E. = (1/2)Mv² + (1/2)(Iω²) where I = (1/2)MR² for a solid cylinder.

Correct Answer: B — (1/2)Mv² + (1/2)(Iω²)

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Q. A wheel of radius R is rolling without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel? (2023)

A. Rω
B. ω/R
C. ω
D. 2Rω

Solution

The linear velocity v of the center of the wheel is given by v = Rω.

Correct Answer: A — Rω

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Q. A wheel rotates with a constant angular acceleration α. If its initial angular velocity is ω₀, what is its angular velocity after time t? (2023)

A. ω₀ + αt
B. ω₀ - αt
C. αt²
D. ω₀t

Solution

Using the equation of motion for rotation, ω = ω₀ + αt.

Correct Answer: A — ω₀ + αt

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Q. A wire of length L and diameter d is stretched by a force F. If the diameter is doubled, what will be the new elongation if the same force is applied? (2019)

A. L/4
B. L/2
C. L
D. 2L

Solution

Elongation is inversely proportional to the area. Doubling the diameter increases the area by a factor of 4, thus elongation becomes L/4.

Correct Answer: B — L/2

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