Question

A piece of wire cut into two pieces A and B and stretched to the same tension and minuted between two rigid walls. Segment A is longer than segment B. Which of the following quantities will always be larger for waves on A than for waves on B

• A. amplitude of the wave
• B. frequency of the fundamental mode
• C. wave velocity
• D. wavelength of fundamental mode

Answer 1

Answer: (D)

frequency $f=\frac{1}{21}\sqrt{\frac{t}{\mu }}$
$f=\frac{v}{\lambda }$
$\Rightarrow \frac{v}{\lambda }=\frac{1}{21}\sqrt{\frac{t}{\mu }}$
$\Rightarrow \lambda =21$
$\lambda \alpha l$
$\Rightarrow$ wavelength of $A$ is larges than that of $B$