Class 11 >> Physics >> oscillations-and-waves >> beats-and-doppler-effect >> explain-doppler-effect-in-sound
Skip to Practice

explain-doppler-effect-in-sound

🚀 The Doppler Effect is a phenomenon observed when there is a relative motion between a source of sound and an observer. It describes the change in frequency (or wavelength) of sound waves as perceived by an observer moving relative to the source of the sound. When the source approaches the observer, the sound waves are compressed, leading to a higher frequency (or pitch). Conversely, when the source moves away, the waves are stretched, resulting in a lower frequency. This effect is commonly experienced in everyday life, such as when an ambulance passes by with its siren on.

Theory Explanation

Understanding Sound Waves

Sound travels in waves, which are characterized by their frequency and wavelength. The frequency is the number of waves that pass a point in one second, while the wavelength is the distance between successive crests of the wave. The speed of sound in air is approximately 343 meters per second at room temperature.

\[ v = f \lambda \]
Relative Motion

The Doppler Effect depends on the relative motion between the source and the observer. If the source is moving towards the observer, the waves are compressed, leading to a higher frequency. If the source is moving away, the waves are stretched, leading to a lower frequency. This can be mathematically expressed as: \( f' = f \frac{v + v_o}{v - v_s} \) where \( f' \) is the observed frequency, \( f \) is the source frequency, \( v \) is the speed of sound, \( v_o \) is the speed of the observer, and \( v_s \) is the speed of the source.

\[ f' = f \frac{v + v_o}{v - v_s} \]
Applications of the Doppler Effect

The Doppler Effect has various applications, including radar and medical imaging (ultrasound). It is also used in astronomy to determine the speed of stars and galaxies relative to Earth by observing the shift in the frequency of light from these objects.

Key Points

  • 🎯 The Doppler Effect occurs due to the relative motion between the source and the observer.
  • 🎯 When the source approaches, the frequency increases; when it moves away, the frequency decreases.
  • 🎯 The formula for the observed frequency incorporates the speeds of both the source and the observer.
  • 🎯 The effect is applicable to all types of waves, including sound and light.
  • 🎯 Real-world applications include radar, medical imaging, and astronomy.

🛠 Simulation is being generated. Please check back in a few moments.

Examples:💡

An ambulance siren emits a sound of frequency 800 Hz. If the ambulance is moving towards a stationary observer at a speed of 30 m/s, calculate the frequency heard by the observer.

Solution:

Step 1: Identify the known values: Source frequency (f) = 800 Hz, speed of sound (v) = 343 m/s, speed of observer (v_o) = 0 m/s, speed of source (v_s) = 30 m/s.

Step 2: Use the Doppler Effect formula: f' = f (v + v_o) / (v - v_s).

\[ f' = 800 \frac{343 + 0}{343 - 30} = 800 \frac{343}{313} \]

Common Mistakes

  • Mistake: Confusing the signs of the speeds in the Doppler Effect formula.

    Correction: Remember that if the source is moving towards the observer, use a positive value for v_s; if moving away, use a negative value.

  • Mistake: Forgetting to convert units when calculating speeds.

    Correction: Always ensure that the speeds are in the same units (e.g., m/s) before substituting them into the formula.

← Back Start Practice