Which equations represent the relationship between wavelength and frequency for a sound wave? Check all that apply.
$v=\lambda f$
$\lambda=v f$
$f=\lambda v$
$\lambda=\frac{v}{f}$
$\lambda=\frac{f}{v}$
$f=\frac{v}{\lambda}$
$f=\frac{\lambda}{v}$
Answer (1)
The fundamental relationship between speed, wavelength, and frequency is v = λ f .
Solving for wavelength gives λ = f v .
Solving for frequency gives f = λ v .
Therefore, the correct equations are v = λ f , λ = f v , and f = λ v .
Explanation
Identifying the Basic Relationship We are given several equations and need to identify which ones correctly describe the relationship between the speed ( v ), wavelength ( λ ), and frequency ( f ) of a sound wave. The fundamental relationship is: v = λ f
Solving for Wavelength We can rearrange this equation to solve for wavelength ( λ ): λ = f v
Solving for Frequency We can also rearrange the original equation to solve for frequency ( f ): f = λ v
Checking the Equations Now, let's check the given equations against our derived equations:
v = λ f - This is the fundamental relationship and is correct.
λ = v f - This is incorrect.
f = λ v - This is incorrect.
λ = f v - This matches our derived equation for wavelength and is correct.
λ = v f - This is incorrect.
f = λ v - This matches our derived equation for frequency and is correct.
f = v λ - This is incorrect.
Examples
Understanding the relationship between the speed, wavelength, and frequency of sound waves is crucial in many real-world applications. For example, when designing musical instruments, engineers need to carefully consider the wavelength and frequency of the sound produced to achieve the desired pitch and tone. Similarly, in medical imaging, ultrasound technology relies on the properties of sound waves to create images of internal organs. By adjusting the frequency and wavelength of the ultrasound waves, doctors can obtain detailed information about the structure and function of different tissues.
