We know that when we pluck a string on an instrument the resulting sound wave tr

Question

We know that when we pluck a string on an instrument the resulting sound wave travels through the air at a speed of (about) 344 m/s. But the wave moving on the STRING itself doesn't have to travel at 344 m/s. Let's consider some of the things that affect the velocity of a standing wave on a string: decide whether each of the following statements are T-True, or F-False. (If the first is T and the rest are F, enter TFFFF) A) Given that waves travel on a mandolin string with speed less than the speed of sound in air, and that a mandolin string vibrates with a wavelength lambda: (T or F) the resulting sound wave produced in the air will have a wavelength longer than lambda. B) The velocity of the wave traveling on a string is higher if you pluck the string with a slightly larger sideways force C) The velocity of a wave traveling on a guitar string is increased if you exchange the string for one that is denser (keeping the length and tension unchanged.) D) Given that waves travel on a violin string with speed less than the speed of sound in air, and that a violin string vibrates with frequency f: (T or F) the fundamental frequency of sound produced by the violin will be higher than f. E) The velocity of the wave traveling on a string stays the same if you increase the length of the string (keeping the type of string, and the tension of the string, unchanged)

Explanation / Answer

The speed of the sound in string is sqrt(T/u)

Where T=tension of force

u=mass per unit length

So the speed of sound depends on the tension and mass per unit length that is how the string is.

A.FAlse. Independent of wavelength.

B.True. SInce velocity is directly dependent on tension

C.False. It is independent of density. No change will be there

D.False. Independent of frequency

E.False. The velocity is dependent on length. So velocity will decrease if we incease the length.

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