In a gas two waves of length 1m and 1.10m have a frequency difference of 10/3 Hz, the velocity of sound is ?
a) 166m/s
b) 332m/s
c) 83m/s
d) 336.7m/s
To find the velocity of sound, we can use the formula:
Velocity = Frequency x Wavelength
Given that the frequency difference is 10/3 Hz and the lengths of the waves are 1m and 1.10m, we can proceed as follows:
Step 1: Calculate the average frequency:
Average frequency = (Frequency of wave 1 + Frequency of wave 2) / 2
= (1 / (wavelength of wave 1) + 1 / (wavelength of wave 2)) / 2
= (1 / 1m + 1 / 1.10m) / 2
Step 2: Calculate the average wavelength:
Average wavelength = (Wavelength of wave 1 + Wavelength of wave 2) / 2
= (1m + 1.10m) / 2
Step 3: Calculate the velocity of sound:
Velocity = Average frequency x Average wavelength
Let's now perform the calculations:
Step 1:
Average frequency = (1 / 1m + 1 / 1.10m) / 2
= (1.10 + 1) / (1m x 1.10m) / 2
= 2.10 / 1.10m^2 / 2
= 1.05 / 1.10m^2
= 0.9545 Hz (approximately)
Step 2:
Average wavelength = (1m + 1.10m) / 2
= 2.10m / 2
= 1.05m
Step 3:
Velocity = Average frequency x Average wavelength
= 0.9545 Hz x 1.05m
= 1.0023 m/s (approximately)
Therefore, the velocity of sound is approximately 1.0023 m/s.
None of the options provided match this value. Please double-check the options or provide additional information.