Question

STATEMENT-1 : When source of sound moves towards a stationary observer the wave length of sound wave reaceived by the observer is different from the wave length of the wave emitted by the source. STATEMENT-2 : The wavelength of the sound wave propagating in the direction of motion of source is smaller than when the source does not move. It is because the source moves by some distance. (1) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1 (2) Statement- 1 is true, statement-2 is true and statement-2 is NOT correct explanation for statement-1 (3) Statement- 1 is true, statement-2 is false (4) Statement- 1 is false, statement- 2 is true

Short answer

Both statements are true, and statement-2 correctly explains statement-1. Answer is (1).

Step-by-step solution

Understand Statement-1

When a source of sound moves towards a stationary observer, the wavelength of the sound waves received by the observer is different from the wavelength of the sound waves emitted by the source. This is due to the Doppler Effect, which explains how the motion of the source affects the observed frequency and wavelength.

Understand Statement-2

Statement-2 states that the wavelength of the sound wave propagating in the direction of the motion of the source is smaller than when the source is not moving. The reason given is that the source moves by some distance.

Evaluate the Truth of Both Statements

Both statements are true. When the source moves towards the observer, the observed wavelength decreases, causing the wavelength to be shorter. This matches with the Doppler effect.

Determine if Statement-2 Explains Statement-1

Evaluate if statement-2 is the correct explanation for statement-1. The source moving by some distance does contribute to the phenomenon explained in statement-1, as the motion of the source relative to the observer leads to a change in the observed wavelength.

Formulate the Answer

Based on the evaluation, we can conclude that both statements are true, and statement-2 provides the correct explanation for statement-1. Therefore, the correct answer is (1).

Key concepts

wavelength

Wavelength is a fundamental concept in understanding waves, including sound waves. It refers to the distance between two consecutive points that are in phase on a wave, such as the distance between two peaks or two troughs. When a sound source moves towards an observer, the wavelength of the sound waves received by the observer gets compressed. This is because the sound waves are 'bunched up' due to the motion of the source. As a result, the wavelength decreases, and the observed frequency increases, which we experience as a higher-pitched sound. Conversely, if the source moves away from the observer, the waves are stretched out, increasing the wavelength and lowering the frequency, resulting in a lower-pitched sound.

Understanding wavelength helps explain the Doppler Effect, a phenomenon observed with all types of waves, including sound and light.

frequency

Frequency refers to the number of wave cycles that pass a point per unit of time, usually measured in Hertz (Hz). It indicates how many waves pass by a point in one second. In the context of sound waves, frequency determines the pitch of the sound we hear. Higher frequencies result in higher-pitched sounds, while lower frequencies produce lower-pitched sounds.

When a sound source approaches a stationary observer, the frequency of the sound waves increases due to the Doppler Effect. This happens because the waves are compressed, resulting in more waves hitting the observer's ear per second. Conversely, when the source moves away, the frequency decreases as the waves are stretched out, leading to a lower pitch.

By examining frequency changes, observers can infer information about the motion of the sound source relative to the observer.

sound waves

Sound waves are longitudinal waves that travel through a medium (like air, water, or solids) by causing the particles of the medium to vibrate parallel to the direction of the wave. These vibrations create compressions and rarefactions, which we perceive as sound. The speed of sound varies depending on the medium through which it travels; for example, sound travels faster in water than in air.

The characteristics of sound waves, including their wavelength and frequency, play a crucial role in the Doppler Effect. When the sound source moves towards an observer, the sound waves get compressed, leading to a higher frequency and shorter wavelength. This causes the pitch of the sound to be higher. When the source moves away, the opposite happens, with the waves stretching out and the pitch lowering.

Sound waves are essential in many technologies and natural processes, such as medical ultrasonography, sonar, and even everyday communication.