Sound WavesHardBloom L3
Question
In a resonance tube experiment, an 80 cm air column is in resonance with a turning fork in first overtone. Which equation can represent correct pressure variation in the air column (x = 0 is the top point of the tube, neglect end correction, speed of sound = 320 m/sec)
Options
A.A sin$\frac{15\pi}{8}$ x cos 600πt
B.A cos$\frac{15\pi}{8}$ x sin 600 πt
C.A cos $\frac{15\pi}{8}$x sin 300 πt
D.A sin $\frac{15\pi}{8}$x sin 300 πt
Solution
Sol. For first overtone
L = $\frac{\lambda}{4} + \frac{\lambda}{2}$
⇒ 80 cm = $\frac{3\lambda}{4}$
⇒ λ = $\frac{3.2}{3}m$
⇒ K = $\frac{2\pi}{\lambda}$ = $\frac{2\pi}{3.2} \times 3$ = $\frac{6\pi}{3.2}$ = $\frac{60\pi}{32}$ = $\frac{15\pi}{8}$
f = $\frac{v}{\lambda}$ = $\frac{320}{(3.2/3)}$ = 300 Hz
⇒ ω = 2πf = 600 π
Hence equation
y = A sin Kx cos ωt = $A\sin\left( \frac{15\pi}{8}x \right)\cos(600\pi t)$
Create a free account to view solution
View Solution FreeMore Sound Waves Questions
A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of15 ms-1. Then, the...Which one of the following does not support the wave nature of light ?...In order that the resultant path on superimposing two mutually perpendicular SHMs be a circle, the condition is that...A tuning fork of frequency 240 Hz vibrates at one end of the tube shown in the figure. If sound is not heard at other en...A person observes a change of 2.5% in frequency of sound of horn of a car. If the car is approaching forward the person ...