Question

Write the equation for the fundamental standing sound waves in a tube that is open at both ends. If the tube is 80 cm long and speed of the wave is 330 m/s. Represent the amplitude of the wave at an antinode by A.

• A. y = A cos (9.93x) sin (1297t)
• B. y = A cos (9.93x) cos (1297t)
• C. y = A sin (9.93x) cos (1297t)
• D. y = A sin (9.93x) sin (1297t)

Answer 1

The correct option is A y = A cos (9.93x) sin (1297t)

Since speed of sound wave=$330m/s$,

$\nu =\frac{v}{2l}=\frac{330}{2\times 0.8}$

Thus $\omega =2\pi \nu =1297$

For a wave, $\frac{\omega }{k}=v$

$⟹k=3.93$

Equation of wave is $y=Acos\left(kx\right)sin\left(\omega t\right)$ since tube is open at both

ends, thus there is an antinode at x=0, and thus there should be the term

$cos\left(kx\right)$ instead of $sin\left(kx\right)$.