Question

a sound wave of wavelength 0.33 m has a time period of 10^-3s.if the time period is decreased by 10^-4 , calculated the wavelength of the new wave

Answer 1

Hey There!!!

For this question, we are going to use the following concepts:

$Frequency=\frac{1}{Time\,\, Period} \,\,\, \implies f=\frac{1}{T} \\ \\ \\ Speed=Wavelength\,\times\, Frequency \,\, \implies v=\lambda f \, \, \implies v=\frac{\lambda}{T}$


Here, the sound is always travelling in the same medium. So, speed of the sound wave is going to be constant. 
So,

$v=constant \\ \\ \\ \implies \frac{\lambda}{T}=constant \\ \\ \\ \implies \frac{\lambda_1}{T_1}=\frac{\lambda_2}{T_2}$


Here, we can take the values as:

$\lambda_1 = 0.33 m \\ \\ T_1 = 10^{-3}s \\ \\ T_2 = 10^{-4}s \\ \\ \lambda_2 =?$


Using the relation we have:


So, we can write a relation


$\frac{\lambda_1}{T_1}=\frac{\lambda_2}{T_2}\\ \\ \\ \implies \frac{0.33}{10^{-3}}=\frac{\lambda_2}{10^{-4}} \\ \\ \\ \implies \lambda_2 = \frac{0.33\times 10^{-4}}{10^{-3}} \\ \\ \\ \implies \boxed{\lambda_2=0.033\,\,metres}$


Thus, the new wavelength is 0.033 metres

Hope it helps
Purva
Brainly Community

Answer 2

time period = T = 10^-3s
wavelength = a = 33×10^-2 m
frequency = f = ?
velocity = v = ?

T = 1/f
fT = 1
f = 1/T
f = 1/10^-3
f = 10³Hz
so frequency of old wave is 10³Hz

then frequency of new wave is 10⁴Hz

velocity= wavelength×frequency
v = an

if one wave time period decrease then it's frequency increase means it's speed constant

af= a¹f¹
33×10^-2× 10³ = 10⁴×a¹
33×10¹/10⁴ = a¹
33×10^-3 = a¹

so wavelength of new wave is 33×10^-3m