Question

Figure shows a stretched string of length $L$ and pipes of length $L, 2 L, L / 2$ and $L / 2$ in options (a), (b), (c) and (d) respectively. The string's tension is adjusted until the speed of waves on the string equals the speed of sound waves in the air. The fundamental mode of oscillation is then set up on the string. In which pipe will the sound produced by the string cause resonance?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Fundamental frequency of wire $\left(f_{\text {wire }}\right)=v / 2 l$

$f=\frac{v}{4 l}, \frac{3 v}{4 l}, \frac{5 v}{4 l}$ cannot match with $f_{\text {wire }}$

$f=\frac{v}{2(2 l)}, \frac{2 v}{2(2 l)}, \frac{3 v}{2(2 l)}$ its second harmonic $\frac{2 v}{2(2 l)}$ matches with $f_{\text {wire - }}$

$f=\frac{v}{2(l / 2)}, \frac{2 v}{2(l / 2)} $ cannot match with $f_{\text {wire }}$

$f=\frac{v}{4(l / 2)}, \frac{3 v}{4(l / 2)}, \cdots$ cannot match with $f_{\text {wire }}$