Question

The vibrations from an 800 Hz tuning fork set up standing waves in a string clamped at both ends. The wave speed in the string is known to be 400 m/s for the tension used. The standing wave is observed to have four antinodes. How long is the string ?

• A. 1 m
• B. 4m
• C. 2m
• D. 3m

Answer 1

The correct option is A 1 m

Frequency of oscillation of string in $n^{th}$ harmonic is $\frac{nc}{2l}$.

where $c$ is the speed of the wave in the string.

Thus $f=\frac{nc}{2l}$

$⟹800=\frac{n\times 400}{2l}$

Since there are four antinodes in the string, $n=4$

Thus $l=1m$