Question 228: Waves

Question

A person observes two moving trains. First reaching the station and another leaves the station with equal speed of $30 \mathrm{~m} / \mathrm{s}$. If both trains emit sounds of frequency 300 Hz , difference of frequencies heard by the person will be (speed of sound in air $330 \mathrm{~m} / \mathrm{s}$ )

Accepted Answer

Frequency of sound heard by the person from approaching train
$$ \mathrm{n}_{\mathrm{a}}=\mathrm{n}\left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right)=300\left(\frac{330}{330-30}\right)=330 \mathrm{~Hz} $$
Frequency of sound heard by the person from receding train
$$ \mathrm{n}_{\mathrm{r}}=\mathrm{n}\left(\frac{\mathrm{v}}{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}\right)=300\left(\frac{330}{330+30}\right)=275 \mathrm{~Hz} $$
Hence, difference of frequencies heard by the person will be
$$ =\mathrm{n}_{\mathrm{a}}-\mathrm{n}_{\mathrm{r}}=330-275=55 \mathrm{~Hz} $$

Answer

80 Hz

Answer

75 Hz

Answer

55 Hz

Answer

45 Hz

Waves

A person observes two moving trains. First reaching the station and another leaves the station with equal speed of 30 \mathrm{~m} / \mathrm{s}. If both trains emit sounds of frequency 300 Hz , difference of frequencies heard by the person will be (speed of sound in air 330 \mathrm{~m} / \mathrm{s} )

Choose the correct answer: