Module 2 : Calculate various properties of sound-wave

Module 2: Properties of Sound

Overview of Sound Properties Calculation

  • Understanding how to determine various properties of sound, including:

    • Frequency

    • Time Period

    • Speed (Velocity)

    • Wavelength

Fundamental Formulas

  • Time Period (T) in seconds:
    T=1fT = \frac{1}{f}
    where:

    • T is the time period

    • f is the frequency

  • Frequency (f) in hertz:
    f=1Tf = \frac{1}{T}
    where:

    • f is the frequency

    • T is the time period

Calculating the Period of a Soundwave

  • Example Calculation for a wave of frequency 50 Hz:

    • Given frequency, calculate the time period using the formula:
      T=1fT = \frac{1}{f}

    • Calculation:

    • T=150T = \frac{1}{50}

    • T=0.020T = 0.020 seconds

Calculating the Frequency of a Soundwave

  • Example Calculation for a wave with a time period of 8.0 seconds:

    • Use the formula:
      f=1Tf = \frac{1}{T}

    • Calculation:

    • f=18f = \frac{1}{8}

    • f=0.125 extHzf = 0.125 \, ext{Hz}

Example: Calculate the Frequency

  • Steps to Calculate Frequency:

    1. Identify the period of the soundwave.

    2. Use the period to determine the frequency.

    3. Apply the formula:
      F=1TF = \frac{1}{T}

    • Calculation:

    • Given period: 0.2 seconds

    • F=10.2F = \frac{1}{0.2}

    • F=5 extHzF = 5 \, ext{Hz}

Speed (Velocity) and Wavelength Formulas

  • Speed (Velocity) of sound:
    v=f×λv = f \times \lambda
    where:

    • v is the speed in metres per second (m/s)

    • f is the frequency in hertz (Hz)

    • λ (lambda) is the wavelength in metres (m)

  • Rearranged forms of the equation:

    • f=vλf = \frac{v}{\lambda}

    • λ=vf\lambda = \frac{v}{f}

Calculating the Speed of a Soundwave

  • Example Calculation:

    • For a frequency of 6 Hz and a wavelength of 3 m:

    • Use the formula:
      v=f×λv = f \times \lambda

    • Calculation:

    • v=6×3v = 6 \times 3

    • v=18 extm/sv = 18 \, ext{m/s}

Frequency Calculation Example

  • Calculate the frequency of a soundwave with a wavelength of 2.0 m and speed of 16 m/s:

    • Use the speed and wavelength relationship:
      f=vλf = \frac{v}{\lambda}

Calculating Wavelength of a Soundwave

  • Example Calculation:

    • For a sound wave in water with a frequency of 300 Hz and a speed of 1500 m/s:

    • Use the rearranged formula:
      λ=vf\lambda = \frac{v}{f}

    • Calculation:

    • λ=1500 extm/s300 extHz\lambda = \frac{1500 \, ext{m/s}}{300 \, ext{Hz}}

    • λ=5 extmetres\lambda = 5 \, ext{metres}

Handling Unknown Variables in Calculations

  • Advice for Problems with Unknown Variables:

    • If the frequency is unknown, you can derive it from the time period to find the speed of the soundwave.

    • Utilize previous knowledge of frequency calculation using the time period to facilitate your calculations.