please need help with thes two questions need full explanation! thanks in advanc

Question

please need help with thes two questions need full explanation! thanks in advance!

1) Standing waves in a string can be produced by oscillating the string at carious natural frequencies. However, in this experiment the string vibrator has only one frequency. How, then, are standing waves with different wavelengths produced?

2) Stringed musical instruments, such as violins and guitars, use stretched strings. Explain (a) how tightening and loosening the strings tunes them to their designated tone pitch or frequency; (b) why the strings of lower tones are thicker or heavier; (c) why notes of higher pitch or frequency are produced when the fingers are placed on the strings.

Explanation / Answer

1)There are standing waves that are integral multiples of the fundamental standing wave.

They all fit into the distance between the fixed end points of the string.

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2) a)For fixed L, resonant lambda is fixed

sqrt[Ft] propotional v propotional F

b)Thicker/heavier strings have greater linear mass density, which isrelated to velocity and therefore frequency as 1 / sqrt[mu] propotional v propotional F

so the greater mu, the smaller f

c) For a given string, the wave velocity is set. Placing a ?nger on astring changes the e?ective length of the string and L = n lambda / 2

If L is shortened, then so is the resonant wavelength. Since v = f lambda

lambda gets smaller, then f must get bigger.

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