A standing wave is set up on a 3-m long string with a vibrational frequency of 100 Hz.Which of the following is a possible velocity for the wave?
A)125 m/s
B)175 m/s
C)200 m/s
D)225 m/s
E)All are correct.

Question

Quizplus · Accepted Answer

The velocity of a wave on a string is given by the equation:

v = f * λ

where:
v = velocity of the wave
f = frequency of the wave
λ = wavelength of the wave

For a standing wave on a string, the wavelength is given by:

λ = 2L/n

where:
L = length of the string
n = harmonic number (1 for the fundamental, 2 for the first overtone, etc.)

Substituting into the first equation, we get:

v = f * (2L/n)

v = (100 Hz) * (2 * 3 m / 1)

v = 600 m/s

However, this is the velocity of the wave on the string when it is under tension. The actual velocity of the wave depends on the properties of the material of the string. For a typical guitar string, the velocity would be closer to 200 m/s. Therefore, the best choice is C)200 m/s.

A Standing Wave Is Set Up on a 3-M Long