Question 31: Waves

Question

The string of length 2 m is fixed at both ends. If the string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of

Accepted Answer

In general, nth mode of a string fixed at ends has frequency,
$$
u=\frac{nv}{2l}$$
where, $$n=1,2,3,...$$
where, $$v$$ is the velocity of wave and $$l$$ is the length of string.
In fourth normal mode, $$n=4$$
$$v=\frac{4
u}{2l}$$
Given, $$
u=500$$ Hz, $$l=2$$ m
Hence, $$500=\frac{4
u}{2	imes2}$$
or, $$v=\frac{500	imes4}{4}=500$$ m/s

Answer

125 m/s

Answer

250 m/s

Answer

500 m/s

Answer

1000 m/s

Waves

The string of length 2 m is fixed at both ends. If the string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of

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