Sound - Ultrasonic and Infrasonic Waves, and their

A SONAR device on a submarine sends out a signal and receives an echo $5\text{ s}$ later. Calculate the distance of the object from the submarine if the speed of sound in seawater is $1530\text{ m/s}$.

Given: Speed of sound ($v$) = $1530\text{ m/s}$, Time ($t$) = $5\text{ s}$. Using the echo-ranging formula: $d = \frac{v \times t}{2}$ $d = \frac{1530 \times 5}{2}$ $d = \frac{7650}{2}$ $d = 3825\text{ m}$

In SONAR, the sound travels to the object and back, covering a total distance of $2d$. To find the one-way distance ($d$), we divide the total distance ($v \times t$) by $2$.

Calculate the wavelength of an ultrasonic wave with a frequency of $40\text{ kHz}$ in air, where the speed of sound is $340\text{ m/s}$.

Given: Frequency ($\nu$) = $40\text{ kHz} = 40,000\text{ Hz}$, Speed ($v$) = $340\text{ m/s}$. Using the formula: $v = \nu \lambda$ $\lambda = \frac{v}{\nu}$ $\lambda = \frac{340}{40000}$ $\lambda = 0.0085\text{ m}$

The wavelength is the ratio of the speed of the wave to its frequency. Here, we must convert kilohertz to hertz before calculation.

A sound source emits a frequency of $15\text{ Hz}$. Is this sound audible to humans? Calculate its time period.

Frequency ($\nu$) = $15\text{ Hz}$. Since $15\text{ Hz} < 20\text{ Hz}$, this is Infrasonic and is not audible to humans. Time period ($T$): $T = \frac{1}{\nu}$ $T = \frac{1}{15}$ $T \approx 0.067\text{ s}$

Human hearing is restricted to $20\text{ Hz} - 20,000\text{ Hz}$. Any frequency below this range is infrasonic. The time period is the reciprocal of frequency.