Acoustics Notes EPHY PDF

# UNIT - I ## ACOUSTICS, ULTRASONICS & DIELECTRICS ### ACOUSTICS #### 1.1 INTRODUCTION TO ACOUSTICS - Acoustics is the science of sound which deals with the generation, reception and propagation of sound. - The acoustical properties of buildings were not studied on a scientific basis till about 190...

# UNIT - I ## ACOUSTICS, ULTRASONICS & DIELECTRICS ### ACOUSTICS #### 1.1 INTRODUCTION TO ACOUSTICS - Acoustics is the science of sound which deals with the generation, reception and propagation of sound. - The acoustical properties of buildings were not studied on a scientific basis till about 1900. - The Fogg Art Museum Hall in Harvard University, U.S.A. was highly defective when it was built. The lectures given in it were not audible to the audience. - Prof. Sabine, Professor of physics in Harvard University, takes the responsibility of eliminating the acoustical defects of the hall. - He found that reverberation was the main cause for a defective quality of hall. Addition of absorbent materials enhances the quality of sound in the hall. Thus, Prof. Sabine laid foundation of acoustic engineering. #### 1.2 REFLECTION OF SOUND (ECHO AND REVERBERATION) **Que. Define echo and reverberation and differentiate between them.** **(A) Echo** - A reflection is called an echo if the time between the original sound and its reflection is long enough so that both the sounds can be heard distinctly. **OR** - Echo is the repetition of sound produced due to reflection of sound by a distant objects like walls, roofs, building, etc. - The sensation of sound persists for about 100 ms after the source stopped giving sound. Hence, in order to heard echo, it must reach the ear 100 ms later than the direct sound. So that the distance of the obstacle from the source is 17m or more, will be heard echo distinctly. **(B) Reverberation** - Reverberation is the persistence of sound even after the source of the sound has stopped. - Reverberation occurs due to multiple reflections of sound. - Reverberation can be experienced in halls without furniture of a newly built house. - **Reverberation Time:** The duration for which the sound persists is called reverberation time. - **Significance of Reverberation Time:** For good acoustics, reverberation time must be optimum. i.e., reverberation time should neither be too short nor too long. - For a hall about 10,000 cu ft. capacity the reverberation time is approx. 1.03 sec. #### 1.2.1 Difference between Echo and Reverberation | Sr. No. | Echo | Reverberation | |---|---|---| | 1 | An echo is a reflection of sound which arrives at the listener sometime after the sound is produced. | Reverberation is defined as persistence of sound after the sound producing source is removed. | | 2 | An echo can be heard in open as well as closed space. | It is usually experienced in closed space. | | 3 | The minimum distance of reflector should be 17.2 meter.| There is no condition of minimum size of room | | 4 | It is used to find depth of sea, ocean, etc. | It is used in musical studio to make sound melodious. | #### 1.3 ABSORPTION COEFFICIENT **Que. Define absorption and absorption coefficient.** - The property of a surface by which sound energy is converted into other form of energy is known as absorption. - The coefficient of absorption 'a' of a material is defined as the ratio of sound energy absorbed by its surface to that the total sound energy incident on the surface. $a = \frac{Sound\ energy\ absorbed\ by\ surface}{Total\ sound\ incident\ on\ surface}$ - In order to compare the relative efficiency of different absorbing surfaces, it is essential to select a standard or reference. Prof. Sabin used a unit area of open window as the standard. Thus, the unit of absorption is the open window unit sabin. A 1m² sabin is the amount of sound absorbed by one square meter area of fully open window. #### 1.4 SABINE'S FORMULA **Que. State Sabine's formula and explain terms involved in it.** - The relation between reverberation time (T), volume of hall (v), area of surfaces (s) and its absorption coefficients (a) is given by Sabine's formula. $T = K\frac{V}{\sum{as}}$ - The reverberation time depends upon the reflecting properties of the wall, floor and ceiling. If they are good reflectors of sound, then sound take longer time to die away and reverberation time of hall would be long. - The reverberation time directly proportional to volume (v) of the hall. i.e., T x v. - The reverberation time is inversely proportional to the surface area of objects. i.e., $T \propto \frac{1}{S}$ OR $T \propto \frac{1}{as}$ - The reverberation time is inversely proportional to the coefficient of absorption of objects. i.e., $T \propto \frac{1}{a}$ OR $T \propto \frac{1}{\sum{as}}$ Where, - K is constant of proportionality, - $S_1, S_2 ...$ = surface area of various objects, - $a_1, a_2 ...$ = coefficient of absorption of various objects. - The value of K will be taken as 0.161 if volume (v) is measured in cubic meter (m³) and surface area (s) is measured in square meter (m²). $T = 0.161 \frac{V}{\sum{as}}$ OR $T = 0.161 \frac{V}{a_1S_1 + a_2S_2 + ... + a_nS_n}$ - The value of K will be 0.05, if volume (v) is measured in cubic feet (f³) and surface area (s) is measured in square feet (f²). $T = 0.05 \frac{V}{\sum{as}}$ #### SOLVED EXAMPLES **Example 1.1:** The volume of a cinema hall is given to be 100m×60m×20m and the total acoustic absorption in it is 6800 metric sabine. Determine the reverberation time in the cinema hall. **Solution:** Given: - Volume of the cinema hall (v) = 100 × 60 × 20 = 120000 m³ - Absorption $∑{as}$ = 6800 metric sabine Find: Reverberation time (T) =? Formula: $T = 0.161 \frac{V}{\sum{as}}$ Calculation: $T = 0.161\frac{120000}{6800}$ $T = 2.84$ sec. Result: The reverberation time in the cinema hall = 2.84 sec. which is approximately equal to 3 sec. **Example 1.2:** A cinema hall has a volume of 7500 m³. The total absorption in the hall is 825 O.W.U. m². What should be the reverberation time? **Solution:** Given: - Total absorption $∑{as}$ = 825 O.W.U.m² - Volume of the hall V = 7500 m³ Find: Reverberation time (T) =? Formula: $T = 0.161 \frac{V}{\sum{as}}$ Calculation: $T = 0.161\frac{7500}{825}$ $T = 1.46$ seconds Result: The reverberation time = 1.46 sec. **Example 1.3:** The volume of an auditorium is 12000 m³. Its reverberation time is 1.5 second. If the average absorption coefficient of interior surfaces is 0.4 sabine m-2. Find the area of interior surfaces. **Solution:** Given: - Volume of the hall (v) = 12000 m³ - Reverberation time (T) = 1.5 second - Average absorption coefficient (a) = 0.4 sabine m-2 Find: Area of interior surfaces (S) =? Formula: $T = 0.161 \frac{V}{\sum{as}}$ $T = 0.161 \frac{V}{as}$ $S = 0.161 \frac{V}{aT}$ Calculation: $T = 0.161 \frac{12000}{0.4 \times 1.5}$ $T = 0.161 \frac{12000}{0.6}$ $T = 0.161 \times 20000$ $T = 3220 m²$ Result: Area of interior surfaces (S) = 3220 m². #### 1.5 ACOUSTICAL PLANNING OF BUILDING AND FACTORS AFFECTING ARCHITECTURAL ACOUSTICS OF BUILDING **Que. What are the conditions for good acoustics. Explain methods of designing for good acoustics.** Acoustics of building is branch of science which deals with planning of building or hall, such that it can provide the best audible sound to the audience. #### 1.5.1 Acoustical Planning of Building or Conditions for Good Acoustics - The reverberation time should be optimum i.e. it should be neither too large nor too small. - The initial sound from the source should be of adequate intensity. The sound should be evenly spread over the whole area covered by the audience. - All the undesired sound should be reduced to the extent that it will not interfere with the normal speech. - The wall, roof and floor of hall should be so designed that to avoid unwanted reflections or echoes. - The total quality of the speech or music must be retained. - Defining the exact purpose for which the room is being put in use. #### 1.5.2 Methods of Design for Good Acoustics **(A) Site Selection** - A proper site with quite surround is to be selected for an auditorium. - It should be away from the busy highway, vehicle traffic, airport, rail traffic or any other noisy location. - For auditorium without air-conditioning require doors and windows to be kept open, the orientation of the hall is such the external noise is maintained at low level. - Where air-conditioning is provided, care should take to reduce the vibrating noise or grill noise. - The noise level in the hall should be kept at around 40 to 45 dB. **(B) Volume** - The volume should be large enough to distribute the sound from source properly. - At 100 Hz frequency the wavelength of sound is 3.4 m. It is expected that dimensions of the hall are much more than this value. - The recommended volumes are - Concert halls = 4.0 to 5.5 m³/person. - Theaters = 4.0 to 5.5 m³/person. - Public lecture hall = 3.5 to 4.5 m³/person. - The height of the hall is determined by the presence and absence of balcony, ventilation requirement, etc. - An average height of 6m for small halls and 7.5 m for large halls. - It is desirable to provide slight increase in the height of ceiling near the center of the hall (for purpose reflection of sound). **(C) Shape and Seating Arrangement** - Usually, a floor plane with side walls with increasing separation is selected for better distribution of sound. - Seats placed of steps of 10-12 cm. The angle of inclination should not be more than 30°, distance of front row should greater than 3 m and last rows should not be greater than 25 m for good visual effect. - The chairs should be arranged in alternate fashion and area spanning around it should be about 0.8 m². - A concave surface within the hall is not desirable because it focuses sound reflections. Such surface much be broken up with smaller convex surfaces so that the sound is diffused in all directions. - The seats should be arranged in concentric arcs and circles. - Sloped floor seating is essential for large audience and good visibility as shown in Fig. 1.1. **(IV) Reverberation** - The reverberation time should be optimum i.e., not be either too long or too short. - A very short reverberation time makes a room dead effect. A long reverberation time gives sound interfering and inaudible. - The optimum value for reverberation time depends on the purpose for which is hall is designed. - A reverberation time of 0.5 sec is acceptable for speeches and lectures, while it is 1 to 2 sec for concerts. - In case of theatres optimum value of reverberation time for small theaters is 1.1 to 1.5 sec whereas for large theaters it may go up to 2.3 sec. **(V) Acoustic Treatment of Interior Surfaces** - The side wall is to be covered with absorbing materials. - Concave shaped ceilings in the form of dome should be avoided. - The floor should be covered with a carpet. Carpet can not only cover a useless reflecting surface bit also greatly reduces audience noise.