A tuba creates a 4th harmonic of frequency 116.5 Hz. When the first
valve is pushed, it opens an extra bit
of tubing 0.721 m long. What is the
new frequency of the 4th harmonic?
(Hint Find the original length.)
(Speed of sound = 343 m/s)
(Unit = Hz)

92.33Hz

Explanation:

A tuba is considered as having one open end and the other end is closed. Then:

f_n = n×v / 4L

so here

Where n = 4

f_4 = 116.5 Hz

116.5 Hz = nv/4L

116.5 Hz = 4v/4L

4×v / 4L = v / L

116.5 Hz = v/L1

Let's assume the speed of sound is 343 m/s. Then substituting 343 m/s for v in equation 1

116.5 Hz = v/L

116.5 Hz = 343 m/s/L

Making L the subject

116.5 Hz × L = 343 m/s

L = 343m/s / 116.5Hz

= 2.944 m

Add 0.721 m to the length, and

f_4 = 343m/s / (2.944+0.721)m

f_4 = 343m/s ÷ 3.715

= 92.328 Hz

Approximately = 92.33Hz

Hence the new frequency for the 4th harmonic is 92.33Hz

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

0.55x745.7j and a calculator