Question

The equation of a travelling plane sound wave is y = 60 sin (456t – 1.2x), where y is in mm and x is in meter. Find the ratio of displacement amplitude with which the particles of media vibrate to the wavelength. Also verify that the maximum particle velocity of vibrating particle of media is equal to velocity of wave times the maximum deformation of media.

Solution

The given travelling wave is,
$straight y equals 55 space sin space left parenthesis 456 straight t minus 1.2 straight x right parenthesis$
On comparing with general wave equation
$space straight y equals straight A space sin left parenthesis ωt minus kx right parenthesis comma$
We get,
$Amplitude comma space straight A equals 55 cm equals 0.55 straight m comma space Angular space velocity comma space straight omega equals 456 space straight s to the power of negative 1 end exponent Wave space vector comma space straight k space equals space 1.2 space straight m to the power of negative 1 end exponent$
Now,
$straight A over straight lambda equals fraction numerator AK over denominator 2 straight pi end fraction equals fraction numerator 0.55 cross times 1.2 over denominator 2 straight pi end fraction equals 0.105$
Maximum particle velocity of media is,
$left parenthesis straight v subscript straight p right parenthesis subscript max equals Aω equals 0.55 cross times 456 space space space space space space space space space space space space space space equals space 250.8 space straight m divided by straight s$ ...(1)
The velocity of wave is,
$straight v subscript straight w equals straight omega over straight k equals fraction numerator 456 over denominator 1.2 end fraction equals 380 space straight m divided by straight s$ ...(2)
Maximum deformation in media,
$open parentheses dy over dx close parentheses subscript max equals Ak equals 0.55 cross times 1.2 space equals space 0.66$
Now,
$straight v subscript straight w open parentheses dy over dx close parentheses subscript max equals 380 cross times 0.66 equals 250.8 straight m divided by straight s$ ...(3)
From (1) and (3),
$space space left parenthesis straight v subscript straight p right parenthesis subscript max equals straight v subscript straight w open parentheses dy over dx close parentheses subscript max space space space space space space space space space space space space space space equals 250.8 straight m divided by straight s$

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

What is sound?

How sound is produced?

Can sound travel in vacuum?

Can two persons hear each other on the moon? Explain.

Can electromagnetic wave propagate in vacuum?

Can we listen in vacuum?

Which of the two moves forward during wave motion - particle or disturbance?

What type of wave is sound wave when it travels in air?

What type of wave is sound wave when it travels in solids?

Which of the two - sound or light is longitudinal in nature?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location