Mechanics | Relativity Answers

A standing wave with wavelength λ = 1.2 m and frequency f = 50 Hz is generated on a stretched cord. For an element of the cord at x = 0.5 m, the maximum transverse velocity is v(y,max) = 2π m/s. The amplitude A of each of the individual waves producing the standing wave is:

0.0125 m

0.03 m

0.02 m

0.01 m

0.025 m

Two identical sinusoidal waves with wavelengths of 1.5 m travel in the same direction at a speed of 10 m/s. If the two waves originate from the same starting point, but with time delay ∆t between them, and with resultant amplitude A_resultant = √3 A then ∆t will be equal to:

0.00625 sec

0.0125 sec

0.025 sec

0.005 sec

0.01 sec

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wo sinusoidal waves of wavelength λ = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the form:

y_res (x,t) = 12(cm) cos⁡(φ/2) sin⁡(150πx-3πt+φ/2).

y_res (x,t) = 12(cm) cos⁡(φ/2) sin⁡(3πx+150πt+φ/2).

y_res (x,t) = 12(cm) cos⁡(φ/2) sin⁡(150πx+3πt+φ/2).

y_res (x,t) = 12(cm) cos⁡(φ/2) sin⁡(3πx-180πt+φ/2).

y_res (x,t) = 12(cm) cos⁡(φ/2) sin⁡(3πx-150πt+φ/2).

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Two identical sinusoidal waves with w

A standing wave has the following wave-function: y(x,t) = 0.2 sin(πx) cos⁡(12πt), where x and y are in meters, and t is in seconds. If the length of the string is L = 2 m and it is fixed at both ends, then the harmonic, n, in which the string is vibrating is:

n = 3

n = 5

n = 4

n = 6

n = 2

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Two sinusoidal waves travelling in the same direction with the same amplitude, wavelength, and speed, interfere with each other to give the resultant wave: y_res (x,t) = 2 cm sin(4πx-60πt+π/3). The amplitude of the individual waves generating this wave is:

8 cm

2/√3 cm

4/√3 cm

4 cm

2 cm

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. If the wave speed is 72 m/s, what is the minimum frequency she should apply to set up standing waves?

20 Hz

12 Hz

24 Hz

15 Hz

18 Hz

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A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. If the wave speed is 72 m/s, what is the minimum frequency she should apply to set up standing waves?

20 Hz

12 Hz

24 Hz

15 Hz

18 Hz

A standing wave has the following wave-function: y(x,t) = 0.2 sin(πx) cos⁡(12πt), where x and y are in meters, and t is in seconds. If the length of the string is L = 2 m and it is fixed at both ends, then the harmonic, n, in which the string is vibrating is:

n = 3

n = 5

n = 4

n = 6

n = 2

The distance between the first and the third nodes of a standing wave is 0.2 m, its maximum displacement is 0.02 m and its frequency is 40 Hz. The wave-functions of the two travelling waves which interfere to give the standing wave are then:

y1 = 0.02 sin⁡(20πx-320πt) ; y2 = 0.02 sin⁡(20πx+320πt),

y1 = 0.01 sin⁡(5πx-40πt) ; y2 = 0.01 sin⁡(5πx+40πt),

y1 = 0.01 sin⁡(10πx-80πt) ; y2 = 0.01 sin⁡(10πx+80πt),

y1 = 0.005 sin⁡(5πx-40πt) ; y2 = 0.005 sin⁡(5πx+40πt),

y1 = 0.04 sin⁡(20πx-320πt) ; y2 = 0.04 sin⁡(20πx+320πt),

A standing wave on a string of length L = 3 m is described by the following equation: y(x,t) = 0.08 sin⁡(2πx) cos(300πt). The fundamental frequency, f1, is:

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