Question

the speed of sound in air is 343 m/s. the speed of sound in water is 1,480 m/s. given that the frequency of a sound wave is 500 hz, you calculate the wavelength of sound in both air and water. based on your calculation, what is the behavior of sound waves in both media? the wavelength stays the same. this shows that the waves speed is consistent in both media. the wavelength increases in water. this shows that the wave speeds up and bends. the wavelength decreases in water. this shows that the wave slows down and bends. the wavelength decreases in water. this shows that the wave loses energy in the medium.

Explanation:

Step1: Recall the wave speed formula

The formula for wave speed \(v\) is \(v = f\lambda\), where \(v\) is the speed, \(f\) is the frequency, and \(\lambda\) is the wavelength. We can rearrange it to \(\lambda=\frac{v}{f}\).

Step2: Calculate wavelength in air

Given \(v_{air} = 343\ m/s\) and \(f = 500\ Hz\). Using \(\lambda=\frac{v}{f}\), we have \(\lambda_{air}=\frac{343}{500}= 0.686\ m\).

Step3: Calculate wavelength in water

Given \(v_{water}=1480\ m/s\) and \(f = 500\ Hz\). Using \(\lambda=\frac{v}{f}\), we have \(\lambda_{water}=\frac{1480}{500}=2.96\ m\).

Step4: Analyze the behavior

Since \(\lambda_{water}>\lambda_{air}\) (because \(v_{water}>v_{air}\) and \(f\) is constant as frequency is determined by the source and does not change with medium), when a sound wave moves from air to water (a denser medium), its speed increases. According to Snell's law for waves (a concept related to wave refraction), when a wave speeds up as it moves into a new medium, it bends.

Answer:

The wavelength increases in water. This shows that the wave speeds up and bends.