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Answer :
When, a violin string is 32.5 cm long having a fundamental frequency of 440 Hz. Then, the speed of the waves on this string is approximately 286 m/s.
The speed of a wave can be calculated using the formula;
speed = wavelength x frequency
For a vibrating string, the fundamental frequency is the frequency at which the string vibrates in its simplest, or fundamental, mode. The wavelength of the fundamental frequency is twice the length of the string, because the string vibrates as a half-wavelength standing wave.
So, the wavelength of the fundamental frequency can be calculated as:
wavelength = 2 x length = 2 x 32.5 cm
= 65 cm = 0.65 m
Substituting the wavelength and the given frequency into the formula, we get;
speed = wavelength x frequency = 0.65 m x 440 Hz
= 286 m/s
Therefore, the speed of the waves on this string is approximately 286 m/s.
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