A 2.30-m-long string is tied at both ends and it vibrates with a fundamental fre

Question

A 2.30-m-long string is tied at both ends and it vibrates with a fundamental frequency of 22 Hz.

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

(express answer in Hz)

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

(express answer in Hz)

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

(express answer in Hz).

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

(express answer in Hz)

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

(express in m/s)

Explanation / Answer

1.

second harmonic frequency

f2=2f1=2*22 =44 Hz

2.

third harmonic frequency

f3=3f1=3*22 =66 Hz

3.

fourth harmonic frequency

f4=4f1=4*22=88 Hz

4.

fifth harmonic frequency

f5=5f =5*22 =110 Hz

5.

wave length

lambda =2L=2*2.3=4.6 m

speed of wave

V=f*lambda =22*4.6=101.2 m/s

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