The frequency of the sound waves is 20 kHz . If the speed of the sound in is \( 1500 \mathrm{~m} \cdot \mathrm{~s}^{-1} \), calculate the wavelength of the sound waves in water.

To calculate the wavelength of sound waves, you can use the formula: \[ \text{Wavelength} (\lambda) = \frac{\text{Speed of Sound} (v)}{\text{Frequency} (f)} \] Given that the speed of sound in water is \(1500 \, \text{m/s}\) and the frequency is \(20 \, \text{kHz} = 20,000 \, \text{Hz}\), you can substitute these values into the formula: \[ \lambda = \frac{1500 \, \text{m/s}}{20000 \, \text{Hz}} = 0.075 \, \text{m} = 7.5 \, \text{cm} \] So, the wavelength of the sound waves in water is \(7.5 \, \text{cm}\). --- Did you know that sound travels faster in water than in air? This is because water is denser than air, allowing sound waves to transmit more quickly. In fact, the speed of sound in air is about \(343 \, \text{m/s}\). So when you're underwater, those little "thuds" can travel much faster! Additionally, this concept isn’t just academic! Understanding sound wavelengths is crucial in various fields, like underwater communication and sonar technology. Submarines utilize these principles to navigate and detect objects, making waves of scientific advancement in marine exploration!