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 = \frac{1}{f}
  where:

  • T is the time period

  • f is the frequency

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

  • Calculation:

  • T = \frac{1}{50}

  • T = 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 = \frac{1}{T}

  • Calculation:

  • f = \frac{1}{8}

  • f = 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 = \frac{1}{T}

  • Calculation:

  • Given period: 0.2 seconds

  • F = \frac{1}{0.2}

  • F = 5 \, ext{Hz}

Speed (Velocity) and Wavelength Formulas

• Speed (Velocity) of sound:
  v = 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 = \frac{v}{\lambda}

  • \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 \times \lambda

  • Calculation:

  • v = 6 \times 3

  • v = 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 = \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:
    \lambda = \frac{v}{f}

  • Calculation:

  • \lambda = \frac{1500 \, ext{m/s}}{300 \, ext{Hz}}

  • \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.