Answer:
5.03 m
Explanation:
The wavelength of a wave is given by
[tex]\lambda=\frac{v}{f}[/tex]
where
v is the speed of the wave
f is the frequency of the wave
For the sonar signal in this problem,
[tex]f=288 Hz[/tex]
[tex]v=1.45\cdot 10^3 m/s[/tex]
Substituting into the equation, we find the wavelength:
[tex]\lambda=\frac{1.45\cdot 10^3 m/s}{288 Hz}=5.03 m[/tex]
Taking into account the definition of wavelength, frecuency and propagation speed, the correct answer is the third option: The wavelength of the sonar signal is 5.03 m.
In first place, wavelength (λ) is one of the parameters used to physically define a wave. This parameter can be defined for any periodic wave, that is, for the type of wave that repeats itself with exactly the same shape every given interval of time.
In a periodic wave the wavelength is the physical distance between two points from which the wave repeats itself. It is expressed in units of length (m).
On the other side, frequency (f) is the number of vibrations that occur in a unit of time, that is, a measure of the number of cycles or repetitions of the wave per unit of time. Its unit is s⁻¹ or hertz (Hz).
Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave's disturbance propagates along its displacement.
Relate the wavelength and the frequency inversely proportional using the following equation:
v = f × λ
In this case, you know:
Replacing:
1.45×10³ m/s= 288 Hz× λ
Solving:
λ= 1.45×10³ m/s÷ 288 Hz
λ= 5.03 m
Finally, the correct answer is the third option: The wavelength of the sonar signal is 5.03 m.
Learn more:
