Which one of the following cannot be the unit of frequency of a sound wave?

Question

Prepp Team · Accepted Answer

Understanding Sound Wave Frequency Units

The question asks us to identify which option cannot be a unit of frequency for a sound wave. Frequency is a fundamental property of a wave, representing how many cycles or oscillations occur in a given unit of time. For sound waves, frequency determines the pitch we perceive.

Let's examine each option provided:

Option 1: dB
Option 2: s^-1
Option 3: Hz
Option 4: min^-1

Analyzing Each Unit Option

We need to determine which of these units is used to measure frequency and which is not.

dB (Decibel): The decibel is a logarithmic unit used to express the ratio of a physical quantity (usually power or intensity) relative to a reference level. In the context of sound, decibels are used to measure sound intensity level or sound pressure level, which relates to the loudness of the sound. Decibels are not a unit of frequency.
s^-1 (Per Second): This unit means 'per second'. Frequency is defined as the number of cycles per unit of time. Therefore, cycles per second is a valid way to express frequency. \( \text{s}^{-1} \) is equivalent to cycles per second. This is a unit of frequency.
Hz (Hertz): The Hertz is the standard SI unit for frequency. One Hertz is defined as one cycle per second. So, \( 1 \text{ Hz} = 1 \text{ cycle/second} = 1 \text{ s}^{-1} \). This is a unit of frequency.
min^-1 (Per Minute): This unit means 'per minute'. Like \( \text{s}^{-1} \), this represents the number of cycles per unit of time (in this case, per minute). While Hertz (per second) is the standard, frequency can be measured in cycles per minute (or rotations per minute - RPM). So, \( \text{min}^{-1} \) is a valid unit of frequency, although not the standard SI unit. This is a unit of frequency.

Conclusion on Sound Wave Frequency Units

Based on the analysis of the units:

s^-1 is a unit of frequency (cycles per second).
Hz is the standard unit of frequency (equal to s^-1).
min^-1 is a unit of frequency (cycles per minute).
dB is a unit of sound intensity or loudness, not frequency.

Therefore, dB cannot be the unit of frequency of a sound wave.

Revision Table: Units in Sound and Waves

Quantity	Common Units	What it Measures
Frequency	Hz, s^-1, min^-1	Number of cycles per unit time (pitch)
Wavelength	meters (m), centimeters (cm)	Distance between two consecutive points in phase
Amplitude	Depends on the wave type (e.g., Pa for sound pressure)	Maximum displacement from the equilibrium position (related to intensity/loudness)
Speed (Wave Speed)	meters per second (m/s)	How fast the wave propagates
Intensity Level	Decibels (dB)	Relative power or intensity of sound (loudness)

Additional Information on Sound Wave Properties

Sound waves are longitudinal mechanical waves. Their properties include:

Frequency: Determines the pitch. Higher frequency means higher pitch. Measured in Hertz (Hz).
Amplitude: Determines the intensity or loudness. Larger amplitude means louder sound. Related to units like Pascals (Pa) for pressure or measured using the decibel (dB) scale for intensity level.
Wavelength (\( \lambda \)): The spatial period of the wave. The distance over which the wave's shape repeats. Measured in meters (m).
Speed (\( v \)): How fast the sound travels through a medium. Depends on the properties of the medium (temperature, density, elasticity). Related to frequency and wavelength by the formula \( v = f \lambda \).
Intensity: The amount of energy the sound wave carries per unit area per unit time. Measured in watts per square meter (\( \text{W/m}^2 \)). The decibel (dB) scale is used to express intensity levels relative to a reference intensity.

It is important to distinguish between these different properties and their respective units when studying sound waves.