A 2.20-m-long string is tied at both ends and it vibrates with a fundamental fre

Question

A 2.20-m-long string is tied at both ends and it vibrates with a fundamental frequency of 21 Hz.

1) Find the frequency of the second harmonic (nn = 2). (Express your answer to two significant figures.)

2)Find the frequency of the third harmonic (nn = 3). (Express your answer to two significant figures.)

3) Find the frequency of the fourth harmonic (nn = 4). (Express your answer to two significant figures.)

4) Find the frequencies of the fifth harmonic (nn = 5). (Express your answer to two significant figures.)

5) What is the speed of waves on the string? (Express your answer to two significant figures.)

Explanation / Answer

Fundamental frequency = 21 Hz

A.

for second harmonic

f2 = n*f0 = 2*21 = 42 Hz

B.

f3 = 3*21 = 63 Hz

C.

f4 = 4*21 = 84 Hz

D.

f5 = 5*21 = 105 Hz

E.

Speed = frequency*wavelength

wavelength = 2*L

Speed = f0*2*L

Speed = 21*2*2.20 = 92.4 m/sec

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