Waves

(i) Here,

So,

(ii) and

, the same.
(original) is the frequency.

Given that
Comparing with general equation of progressive wave, we get


or or

From the figure for sound travel
Given,

Time for the echo s
Velocity of the plane
Here,
velocity of sound

Frequency is given by First frequency and second frequency Hence, the ratio of frequencies

Given, velocity of sound,
Velocity of listner,
Velocity of source
Frequency of horn emitted

The apparent frequency


On solving we get

By using the relation,
We have,
The phase difference,

For an open pipe, the frequency

We are given the equation of a stationary wave along a stretched string: % Step 1: General Form of a Stationary Wave The general equation of a stationary wave is of the form: where: - is the amplitude of the wave, - is the wave number, - is the angular frequency, - is the position along the string, - is the time. In this case, comparing the given equation with the general form: We identify: - The amplitude , - The wave number , - The angular frequency . % Step 2: Distance Between Adjacent Nodes In a stationary wave, nodes are points where the displacement is always zero. These occur when the sine term is zero. Thus, the condition for a node is: The general solution to this is: Solving for , we get: Thus, the nodes are located at . The separation between two adjacent nodes is the distance between two consecutive values of . For example, the distance between and is: Thus, the correct answer is 3 cm.