This problem asks us to find the time (\(t\)) it takes for a sound wave to travel a specific distance, given its frequency (\(f\)). We need to use the fundamental relationships between wave speed, frequency, wavelength, distance, and time.
Before calculating, let's recall the key properties of waves involved:
The problem provides us with:
We need to determine the value of \(t\). We can use two main formulas for wave speed (\(v\)):
We are given that the distance \(d = 150 \lambda\). Let's substitute this into the second speed formula:
\(v = \frac{150 \lambda}{t}\)
Now, since the wave is traveling in a single medium, its speed (\(v\)) must be constant. Therefore, we can set the two expressions for \(v\) equal to each other:
\(f \lambda = \frac{150 \lambda}{t}\)
Notice that the wavelength (\(\lambda\)) appears on both sides of the equation. Since \(\lambda\) must be greater than zero for a wave to exist, we can cancel it out:
\(f = \frac{150}{t}\)
Our goal is to find the time \(t\). We can rearrange the equation to isolate \(t\):
\(t = \frac{150}{f}\)
Finally, we can substitute the given frequency value (\(f = 300\) Hz) into this equation:
\(t = \frac{150}{300 \text{ Hz}}\)
Calculating the value:
\(t = 0.5 \text{ s}\)
The calculation shows that the sound wave travels the specified distance in 0.5 seconds.
The term "Terminal High Altitude Area Defense" sometimes mentioned in news, refers to
The Defence Research & Development Organisation (DRDO) recently conducted a successful flight-test of the Pinaka Long Range Guided Rocket (LRGR). The rocket was tested for a user-defined minimum range of what distance?
Which among of the following missiles is called the Indian Patriot?
What is the name of the Anti-Radiation Missile tested by India in October 2020 from a Su-30 MKI fighter aircraft?
Where were the field evaluation trials of the Anti-Tank Guided Missile (ATGM)-Nag Mk 2 conducted?
How many targets can Bhargavastra missile system engage simultaneously?