question_answer

A man \[x\]can hear upto 10 kHz and another man \[y\]upto 2 kHz. A note of frequency 500 Hz is produced before them from a stretched string then both will hear sounds of:

A)  different pitch but same quality

B)  same pitch but different quality

C)  same pitch and same quality

D)  different pitch and different quality.

Correct Answer: B

Solution :

  \[V=100\,V\] \[i=1\,\text{amp}\] \[V=iR\] \[R=\frac{100}{1}\] \[=100\,\Omega \] \[{{V}_{a.c.}}=100\,V\] \[Z=\sqrt{{{R}^{2}}+X_{L}^{2}}\] \[i=0.5\,\text{amp}\] \[V=\sqrt{({{R}^{2}}+X_{L}^{2})}\] \[\frac{1000}{5}=\sqrt{{{R}^{2}}+X_{L}^{2}}\] \[{{(200)}^{2}}={{100}^{2}}+{{X}_{L}}^{2}\] \[40,000-10,000={{X}_{L}}^{2}\] \[\sqrt{30,000}={{X}_{L}}\] \[{{X}_{L}}=173.2\,\Omega \] \[{{X}_{L}}=2\pi f\,L\] \[173.2=2\pi \times 50L\] \[L=0.551\,H\]