A wave equation which given the dispplacement along the y-direction is given by ,
`y = 10^(-4)sin (60t +2x)`
where x and y are in matre and t is time in second. This represents a wave

Options

A. travelling with a velocity of 30 m/s in the negative x- direction
B. of wavelength `(pi)`m
C. of frequency 30/`(pi)` Hz
D. of amplitube `10^(-4)`

Answer

To solve the given wave equation \( y = 10^{-4} \sin(60t + 2x) \), we will analyze the parameters of the wave step by step.

### Step 1: Identify the wave parameters
The general form of a wave traveling in the negative x-direction is given by:
\[ y = A \sin(\omega t + kx) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

From the given equation \( y = 10^{-4} \sin(60t + 2x) \), we can identify:
- Amplitude \( A = 10^{-4} \)
- Angular frequency \( \omega = 60 \)
- Wave number \( k = 2 \)

### Step 2: Calculate the wave velocity
The wave velocity \( v \) can be calculated using the formula:
\[ v = \frac{\omega}{k} \]
Substituting the values of \( \omega \) and \( k \):
\[ v = \frac{60}{2} = 30 \, \text{m/s} \]

### Step 3: Calculate the wavelength
The wavelength \( \lambda \) can be calculated using the formula:
\[ \lambda = \frac{2\pi}{k} \]
Substituting the value of \( k \):
\[ \lambda = \frac{2\pi}{2} = \pi \, \text{m} \]

### Step 4: Calculate the frequency
The frequency \( f \) can be calculated using the formula:
\[ f = \frac{\omega}{2\pi} \]
Substituting the value of \( \omega \):
\[ f = \frac{60}{2\pi} = \frac{30}{\pi} \, \text{Hz} \]

### Summary of Results
- Amplitude \( A = 10^{-4} \)
- Wave velocity \( v = 30 \, \text{m/s} \)
- Wavelength \( \lambda = \pi \, \text{m} \)
- Frequency \( f = \frac{30}{\pi} \, \text{Hz} \)

### Conclusion
All four options given in the question are correct:
1. The wave travels with a velocity of 30 m/s in the negative x-direction.
2. The wavelength is \( \pi \, \text{m} \).
3. The frequency is \( \frac{30}{\pi} \, \text{Hz} \).
4. The amplitude is \( 10^{-4} \).