Question

The equation of a progressive wave is y = 8sin [2π (t/0.05-0.5x ) +2 ] cm
find the amplitude, frequency, Velocity, Wavelength and wave number?​

Answer 1

11th/Physics

Waves

Answer :

The equation of a progressive wave is given by

• y = 8sin[2π(t/0.05 - 0.5x)+2] cm

We have to find

• Amplitude
• Frequency
• Velocity
• Wavelength
• Wave number

★ A plane progressive harmonic wave travelling along positive direction at x-axis can be represented by

• y = A sin 2π (t/T - x/λ + ∅)

A denotes amplitude

T denotes time period

t denotes time

x denotes distance

λ denotes wavelength

∅ denotes phase

1) Amplitude :

It is clear from the given equation that

• Amplitude (A) = 8 cm

2) Frequency :

From the given equation, 1/λ = 0.5

We know that, frequency is the reciprocal of the wavelength$.$

➠ f = 1/λ

➠ f = 0.5 Hz

3) Velocity :

Velocity of wave is given by

• v = f × λ

Here, f = 0.5 Hz and λ = 2cm

➠ v = f × λ

➠ v = 0.5 × 2

➠ v = 1 cm/s or 0.01 m/s

4) Wavelength :

Refer to the point (2)

➠ 1/λ = 0.5

➠ λ = 1/0.5

➠ λ = 2 cm

5) Wave number :

Wave number (k) = 2π/λ

➠ k = 2π/2

➠ k = π

➠ k = 3.14 cm‾¹

Answer 2

Explanation:

previous answer there write as wrong that frequency is reciprocal to the wavelength.actually wave number is reciprocal to the wave length.hence in the previous answer frequency is wrong.but I thought that how can th specialist verify the answer.