Question

Two tuning forks A and B are sounded together and 7 beats/s are heard. A is in resonance with a 32 cm air column closed at one end and B is in resonance when length of air column is increased by 1 cm. The frequencies of forks A and B are

• A. 264 Hz, 256 Hz
• B. 272 Hz, 264 Hz
• C. 231 Hz, 224 Hz
• D. 220 Hz, 512 Hz

Answer 1

Answer: (C)

231 Hz, 224 Hz

Tuning fork A :
Length of closed air column $L_A=32cm=0.32m$
Frequency of tuning fork A ${\nu }_A=\frac{v}{4L_A}=\frac{v}{4\left(0.32\right)}$
Tuning fork B :
Length of closed air column $L_B=33cm=0.33m$
Frequency of tuning fork B ${\nu }_B=\frac{v}{4L_B}=\frac{v}{4\left(0.33\right)}$
Beat frequency $b={\nu }_A-{\nu }_B$
$\therefore$ $7=\frac{v}{4\left(0.32\right)}-\frac{v}{4\left(0.33\right)}$
$⟹$ $v=295.7m/s$
Frequency of tuning fork A ${\nu }_A=\frac{295.7}{4\left(0.32\right)}=231Hz$
Frequency of tuning fork B ${\nu }_B=\frac{295.7}{4\left(0.33\right)}=224Hz$