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Two waves of wavelength 1m & 1.01 m produce 10 beats in 3 sec. The velocity of sound in a gas is about
- a)300 m/s
- b)337 m/sec
- c)33 m/s
- d)1120 m/sec
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two waves of wavelength 1m & 1.01 m produce 10 beats in 3 sec. The...
As we know wavelength= spped/frequency
Wavelength 1= 1m
Wavelength 2= 1.01m
=> 1=v/f1
f1= v
1.01=v/f2
f2= v/1.01
Now beat is 19 beats /3 sec
f1 - f2= 10/3
Solving equations we get
v=336.6m/s
Most Upvoted Answer
Two waves of wavelength 1m & 1.01 m produce 10 beats in 3 sec. The...
Solution
Given, $\lambda_1=1m$, $\lambda_2=1.01m$, $n=10$ and $t=3s$
Let the frequency of wave 1 be $f_1$, then frequency of wave 2 will be $f_2=f_1-\frac{n}{t}$
We know that $v=f\lambda$
Calculating velocities of wave 1 and wave 2, we get
$v_1=f_1\lambda_1$
$v_2=f_2\lambda_2$
Substituting the values of $f_2$ and $f_1$, we get
$v_2=(f_1-\frac{n}{t})\lambda_2$
$v_1=f_1\lambda_1$
We know that velocity of sound in gas is given by $v=\sqrt{\gamma RT}$
Where, $\gamma$ is the adiabatic constant, $R$ is the gas constant, $T$ is the temperature in Kelvin
Assuming the gas to be air at room temperature, we get $\gamma=1.4$, $R=287 J/kgK$, $T=293K$
Substituting these values, we get
$v=\sqrt{\gamma RT}$
$v=\sqrt{1.4\times287\times293}$
$v=337 m/s$
Therefore, option (b) is the correct answer.
Given, $\lambda_1=1m$, $\lambda_2=1.01m$, $n=10$ and $t=3s$
Let the frequency of wave 1 be $f_1$, then frequency of wave 2 will be $f_2=f_1-\frac{n}{t}$
We know that $v=f\lambda$
Calculating velocities of wave 1 and wave 2, we get
$v_1=f_1\lambda_1$
$v_2=f_2\lambda_2$
Substituting the values of $f_2$ and $f_1$, we get
$v_2=(f_1-\frac{n}{t})\lambda_2$
$v_1=f_1\lambda_1$
We know that velocity of sound in gas is given by $v=\sqrt{\gamma RT}$
Where, $\gamma$ is the adiabatic constant, $R$ is the gas constant, $T$ is the temperature in Kelvin
Assuming the gas to be air at room temperature, we get $\gamma=1.4$, $R=287 J/kgK$, $T=293K$
Substituting these values, we get
$v=\sqrt{\gamma RT}$
$v=\sqrt{1.4\times287\times293}$
$v=337 m/s$
Therefore, option (b) is the correct answer.
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